Piezoelectric crystal element



' Dec. 8, 1942.

2 Sheets-Sheet 2 20' IN 17/1501 //V6// nventor Patented Dec. 8, 1942PIEZOELECTRIC CRYSTAL ELEMENT Paul D. Gerber, Woodl-ynne, N. 1., minorto Rs dio Corporation of America,

Delaware a corporation oi Application January 31, 1940, Serial No.316,612

4 Claims.

This invention relates to the art of cutting quartz piezo-electrlcelements of the type that exhibits a shear type of thickness vibration.Thus, it will be understood that the invention herein described isapplicable to all thicknessmode quartz blanks or elements wherein theelectrode or major faces are tilted with respect to the optic (Z) axisof the mother crystal (see British Patent 457,342 of 1936), as well asto so-called Y-cut crystals (see Tillyerl,90'7,6l3) and to X+ crystals(see Bokovoy 2,176,653), but is not applicable to X-cut crystals (seeTaylor and Crossly 1,72%232).- (As is now appreciated by those skilledin the art, X-cut crystals exhibit a "longitudinal type of thicknessvibration.)

The ordinary electrical constants (e. g., resistance, capacitance andinductance) have their equivalents in quartz. These equivalent constantsor characteristics are known to those skilled in the art and, in anyevent, can be readily ascertained in the case of a given element. Thus,a technician confronted with two piezoent invention is to provide ashear type thick- I mess-mode crystal which shall exhibit (a) theoptimum piezo-electrie effect, (b) a unitary free dom for" itsthickness-mode of vibration, and.

(c) one which is nevertheless of a size approximating thatsuggestecl,for example, by the electrical constants of the circuit or by the sizeof the holder or other apparatus in which or with which it is to beused.

electric elements having the same thicknessmode frequency but ofdifferent length-breadth dimensions can readily ascertain which of thetwo is the better adapted, lectrically, for use in a circuit havingknown circuit constants. The trouble with this procedure is that hiscalculations may dictate the use of a crystal element whosepiezo-electric properties are unsuited for the particular task in hand.By way of example, the crystal selected by this procedure may ex" hibita relatively weak piezo-electric effect or its operation may becharacterized by the presence of disturbing spurious frequencies. Thesame objections obviously obtain when one calculates in advance thedimensions required to endow a crystal blank with the electrical (asdistinguished from piezo-electrlcal) characteristics necessary to matchit to a particular circuit.

Considered from another aspect: It would be of considerable advantage tothe manufacturer of thickness-mode crystals if he could adopt certainlength-breadth dimensions as a. standard not only for his crystals butalso for the holders or mountings therefor, and could adhere to such,

standard dimensions substantially irrespective of the frequencies of thevarious crystal elements which he is called upon to produce. But suchstandardization has heretofore been thought impossible of practicalachievement since, as previously indicated, of two crystal elementshaving the same length and breadth dimensions but oi differentthickness-mode frequencies, the one may exhibit excellentplezo-electrlcproperties Other objects and advantages, together withcertain preferred methods of procedure for carrying the invention intoeffect, are brought out in the specification and in the accompanyingdrawings, wherein Figure 1 is a quartz bar from which three blanks ofdifferent known orientations have been cut, and

Figures 2 and 3 comprise a family of curves which, when fitted togetherby placing Fig. 3 under and in register with Fig. 2, form a chart wnichwill be referred to in explaining the practice of the invention.

The present invention teaches that if a shear type thickness-mode quartzpiezo-electric crystal element is so dimensioned that its width bearsany one of certain given dimensional ratios with respect toitsthickness, then, and then only, will the finished element exhibit (a)its optimum or maximum useful piezo-electric effect and (h) substantialfreedom from undesired or "spurious" thickness-mode frequencies.

in carrying the invention into effect, it is nec essary to know the"standard frequency constant- (K) for thin plates, of the particularcrystal blank to which the invention is to be applied. Unfortunately,the published tables of frequency constants now available are not alwaysin agreement. This may be so because the tables are based in part uponmathematical calculations which, more often than not, are figured forblanks of a single size, whereas the fact 0! the matter is that blanksof different sizes exhibit slightly different constants. Accordingly,where there is any doubt as to the value of K, the techv niciandesiringto practice the invention should,

and compute its constant (K) in agreement with the well-known formulaK=j times t (1) where f is the fundamental thickness-mode frequency ofthe blank expressed in megacycles, and t is the thickness of the blankmeasured in mils (thousandths) of an inch. The constant (K) thusobtained is the "standard constant to which reference is made in thefollowing examples.

, Referring now to Fig. 1. The "standard frequency constants (K) for thethin quartz blanks VI, and V2 are Vi, K equals 66 Y, K equals 78 V2, Kequals 99 Each of these blanks is of a known orientation. The centerblank Y is a Y-cut blank (see Tillyer 1,907,613) and the blanks Vi andV2 are so called V-cut blanks, which, as described in the aforesaidBritish Patent 457,342 exhibit a very low temperature cceflicient offrequency.

The blank Vi has its major or electrode faces rotated substantially 3430about 9. 1+0 axis which is normal to a reference axis X+6 which liessubstantially 25 removed from an X-axis in the "ii- I plane. Thedirection of rotation is toward parallelism with the plane of a minor(12.

face (not shown) of the mother crystal. orientation of the blank Vi may,accordingly, be expressed as follows:

The blank V2 has its major or electrode faces rotated substantially 48about a reference axis 5+0 which is normal to a reference aids X+0 whichlies substantially 25 removed from an X- axis in the X-Y plane. Thedirection of rotation is toward parallelism vdth theplane of a major (m)apes; face (not shown) of the mother crystal. The orientation of theblank V2 ma accordingly, be expressed as follows:

Using the same symbols, the orientation of the Y-cut (or Tillyer-cut or30-angle cut) blank Y of Fig. 1 may be described as follows:

That dimension of the blanks Vi and V2 which lies-along the referenceaxis Y+0 is hereinafter referred to as the "width dimension. The lengthdimension of each of these blanks Vi and V2 thus lies along a 2+0 axisand the thickness dimension is in the general direction of the X+6 axis.

' The width dimension of the Y-cut blank lies along an X-axis and thelength dimension lies along the Z-axis.

EXAMPLE No. 1

The problem: To determine how the quartz blank VI of Fig. 1 should befinished to provide a piezo-electric resonator or oscillator (of anydesired frequency) which shall exhibit all three (a, b, and c) of thecharacteristics described in the fourth paragraph of this specification.

As previously set forth, the standard frequency constant (K) for blanksof the orientation of the blank VI is 66. All of the other informationnecessary to the solution of the foregoing problem is contained in Figs.2 and 3 which, when joined (by placing Fig. 3 beneath Fig. 2) comprise asingle chart.

This chart shows a family of curves which are separately numbered 1 to50 inclusive. Each curve is individual to a crystal element whose widthis some multiple (usually not an integral multiple) of its thicknessdimension. The chart =is callbrated along its abscissa (in Fig. 3) interms of mils of an inch of the width dimension of a crystal elementwhose length dimension will be understood to be 1 inch, or thereabouts.The left ordinate of the chart is calibrated for frequency in terms ofmegacycles and fractions of a megacycle. The right ordinate of th charthas been marked to indicate the constants peculiar to crystals of thedescribed VI orientation. (As will hereinafter more fully appear, whenthis chart is employed in the design of crystal elements of otherorientations, the calibration of the bottom scale and the values of Kmay be changed to suit crystal elements of that particular orientation.)

A technician, in using the chart of Figs. 2 and 3 and desiring to make afinished piezo-electric element or oscillator of a particular frequencyfrom the quartz blank Vi of Fig. 1, may first select the desiredfrequency on the left-hand ordinate of the chart. By way of example, letus assume that a frequency of, say, .I of amegacycle (i. e., 700 kcs.)is selected, as indicated at A in Fig. 3. Now, if a line B is projectedat a right angle across this chart and a perpendicular line C is movedacross the chart to each point where the line B intersects these curves,one may read at the bottom of the chart a number of different widthdimensions, any one of which will ensure a filllsl'lE-d '7 kc. elementpossessing the desired characteristics. More specifically, this chartshows that 700 kc. VI type crystal will exhibit the foregoing desirablecharacteristics provided that its width is of any of the followingdimensions, as expressed in mils of an inch: 275; 42%; 5'72; 712; v863;1010; i; 1302; 1458; 1606; a and 1910.

if the crystal is finished to a width other than above indicated, itsamplitude of vibration and its freedom from spurious frequencieswill bemore or less directly proportional to the degree of departure from thesedimensions. Thus, the weakest response and the most disturbing spuriousfrequencies will ordinarily be present in a crystal whose widthdimension falls midway between any two successive dimehsions in theabove summary of dimensions.

An even greater choice of suitable width dimensions can be obtainedsimply by extending the abscissa and curves of the chart. Such extensionhas been omitted in the interests of brevity since it is very seldomthat one desires to make a crystal element of a-width more thansubstantially two inches. Obviously, one practicing the invention mayselect that width of crystal most nearly suited for the particularcircuit or holder in which the element is to be used.

The thickness dimension required to endow the blank with the particularfrequency desired remains to be calculated. It has been determined inreducing the invention to practice that the value of K is fixed in thecase of all crystals wherein the width is'more than approximatelyfourteen (say, 13.88) times the thickness dimension but varies in thecase of crystals wherein the width dimension is less than substantiallyfourteen times the thickness dimension. The variation in the case of thedescribed V1 type of crystal element is indicated by the values of Kmarked along the right-hand ordinate of Fig. 3.

Thus, to determine the exact thickness dimension for any V1 typeelement, the value 01' K for the particular width dimension desired maybe selected from the said right-hand scale. By way of example, it ablank whose width dimension is. say, 1302 mils of an inch is selectedfor flnishing, its frequency constant K is equal to 66 (indicatedadjacent curve 9), whereas one whose width is, say, 424 mils of an inchhas a frequency constant (indicated adjacent curve No. 3') of K=68.6.Substituting these values of K in the well-known formula it will be seenthat the exact thickness of a 700 kc. V1 type crystal whose width is1302 mils should be approximately 94.3 mils of an inch, whereas thethickness dimension of a similar blank 424 mils wide should beapproximately 98 mils of an inch.

Exanrrse No. 2

Referring still to the chart of Figs. 2 and '3, it can be shown that theratio of width to thickness of any crystal whose dimensions are dictatedby a particular curve of this chart are as follows:

Table #3 sassssa'ssassssssssessscee sssasseaeaseeeeasaeesseasassssssssssssassassaws 83E$8388$888$33$8$8$3$ In applying the inventionto a crystal blank 01' an orientation other than a V1 blank (Example 1)it is first necessary to ascertain the "standard" frequency constant (K)which obtains for the particular orientation of the blank which has beenselected for finishing. As previously set iorth, the "standard frequencyconstant is that constant which obtains in all blanks (of the sameorientation) whose width is 13.88 or more times its thickness dimension.

The standard" frequency constant for crystal blanks of the orientationof blank V2 of Fig. 1 is K=99.

For crystals having a width less than 13.88 times the thicknessdimension the frequency constant (hereinafter occasionally designated K)varies in the same ratio as it does in the case of the standardfrequency constant given in the chart of Figs. 2 and 3. The followingtable of correction factors" (5) for the standard Irequncy constant hasbeen derived from the said chart.

Table #4 cum time? Let us now assume that it is desired to make a 1megacycle oscillator from the blank V2 of Fig. 1. Let us also assume(for one or the reasons heretofore given) that it is desired that thefinished plate be about one inch square, i. e., as near to thesedimensions as it is possible to make an oscillator which exhibits (a)the optimum piezo-eiectric effect, and (b) a unitary freedom for itsthickness-mode of vibration.

As above mentioned the standard frequency constant for the blank VtisK=90. We know that the length dimension is not critical and may beexactly 1 inch, if desired. It is also apparent that in order to obtainan oscillating crystal whose width is approximately one inch, a widthto-thickness ratio of or 10.1 should be employed. Reference to theforegoing Table #3, however, shows that this exact width-to-thicknessratio does not appear on this table, that is to say, ii the width dimen'sion of a V2, 1 megacycle blank were to be made 10.1 times itsthickness dimension, the finished element would not exhibit thecharacteristics (a and b) desired. It is accordingly necessary to selectfrom the said Table #3 that width-tothickness ratio which most nearlyapproximates 10.1, i. e. 10.68. It will be observed from an inspectionof the said Table #3 that this ratio of 10.68 is peculiarto curve 7 ofthe chart of Figs. 2 and 3.

Having identified the number at the mode or curve of the finished blank(i. e., curve No. 7) it now remains to determine the substantially exactthickness and width dimensions required to achieve the desired.- 1megacycle oscillator. The thickness dimension is determined by theformula K tllfllefl 3 (5} where f==the desired frequency of i megacycle,K=the standard frequency constant (99) and. S=a correction factor which,for the seventh "mode or curve, is shown (in Table #4) to be 1.004.Therefore:

or, solved, thickness=approximately 99.4 milsoi an inch.

Finally, to ascertain the width dimension, it is necessary to multiplythe thickness dimension 99.4 by the width-tothickness ratio peculiar tothe mode or curve No. i. As shown in Table 3, this ratio is 10.68, hencethe width dimension of the finished element should be 99.4 times 10.6 orapproximately 1062 mils oi an inch.

ExAMPLnNo. 3

Let us assume that it is desired to finish the Y-cut blank'oi Fig. 1 toprovide an oscillator haying a single thickness-mode response of, say1500 kc. Assume, further, it is desired that the finished element be asnear to .5" width, by 1" length, as is possible for an elementpossessing the desired characteristics (a and b) to be.

We know that the standard frequency constant of a Y-cut blank is 78.Therefore, the thickness of a blank constructed in agreement withFormula No. 2

I would be 52 mils of an inch. Following the procedure outline inExample No. 2, we find the approximate ratio in this case to beapproximately 9.62. Referring to Table 3, we find that the ratio whichis closest to 9.62 on this table is the one given in connection withcurve or mode 6, i. e., 9.98. Having identified the number of the modeor curve (i. e. curve No. 6) of the finished blank, it now remains todetermine the substantially exact thickness and width dimensionsrequired to achieve the desired 1500 kc. response. As in Example 2, thethickness dimension is determined by Formula No. 5, i. e., i=1 times S,divided by f=l.5 (niegacycles), K=78, and S is the correction factorwhich, for the 6th mode or curve is shown in Table No. i to be 1.008.Therefore I or, solved, thickness dimension=apprcximately 52.4 mils ofan inch.

Finally, order to ascertain the width dimension, it is necessary tomultiply the thickness dimension of 52. mils of an inch by thewidthto-thickness ratio peculiar to the mode or curve No. 6. [as shownin Table No. 3, this ratio is 9.68; hence, the width dimension of theY-cut blank of Fig. 1 when finished to a frequency of 1.5 megacyclesshould be approximately 476 mils of an inch.

The invention is obviously not limited to any particular manner ofcutting, grinding, lapping or finishing the quartz blank or elements.

It is well known in the art that in order to obtain a. desired frequencycharacteristic in a plezo-electric quartz element with a nice degree ofprecision, frequent tests should be made between successive stages of'the finishing operation. Such tests may indicate minor departures fromthe tables, charts and graphs of this specification. Accordingly, theinvention is not to be limited except insofar as is necessitated by theprior art and by the spirit of the appended claims.

What is claimed is:

1. A piezo-electric quartz element adapted to respond to a predeterminedthickness shear-mode requency and having a width to thickness ratioselected from Table No. 3 01' the accompanying specification, thethickness dimension oi said element measured in mils of an inch beingsubstantially that dictated by the formula where f is the said thicknessshear-mode frequency of said element, K is the standard frequencyconstant for a quartz blank of the same orientation, and S is a factorpeculiar to the said width-to-thickness ratio, the value of said factorbeing substantially that indicated in Table No. 4 of the accompanyingspecification.

2. The invention as set forth in claim 1 and wherein K is equal tosubstantially 66.

3. The invention as set forth in claim, 1 and wherein X is equal tosubstantially 78.

4. The invention as set forth in claim 1 wherein K is equal tosubstantially 99.

and

PAUL D. GERBER.

